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Ch. 2: Concepts, Assumptions, and Models
I. Concepts and Features
A. An examinee’s performance on a test is a monotonically increasing function of a
set of latent traits or abilities.
B. The item characteristic curve (ICC) describes the function between an examinee’s
performance on a test item and the latent trait.
C. The IRT model was adopted from psychophysics (threshold) and biology (lethal
dose). OHP.
D. The IRT models are falsifiable models.
E. The IRT models offer the possibility of computing invariant item and person
parameters.
II. Assumptions
A. Unidimensionality of the latent space
1. Only one latent trait is measured by items in one test.
2. In reality, if items in one test measure one dominant latent trait, the
unidimensionality assumption is met.
3. Multi-dimensional IRT models can be developed, Mulaik (1972) and
Samejima (1974).
4. Factor analysis can be used to test the unidimensionality assumption.
B. Local Independence (Conditional Independence)
1. For a given ability level, the probability of getting one item correct is
independent of the probability of getting other items correct.
P(ui = 1 uj = 1| ) = P(ui = 1| )P(uj = 1| ), i j
2. If we partial out the effect of ability ( ), then, the probability of getting
the items correct is independent of each other.
3. The ability specified in the model is the only factor influencing an
examinee’s performance.
4. If we meet the unidimensionality assumption, then the complete latent
space has only one trait.
5. Even though latent space has multiple traits (multi-dimensionality), as
long as all traits are specified in the model, the local independence
assumption will hold.
6. If one item is related to another item (cue or hint), the local independence
assumption will not hold.
III. IRT models
A. Two mathematical Models
1. Normal Ogive Models: utilize the cumulative normal curve.
2. Logistic Models: mathematically simpler than the Normal Ogive Models,
but the practical difference from the N.O.M. is less than .01 (OHP for
ICC).
B. Normal Ogive Models: by Lord (1952)
1. One-parameter Normal Ogive Model
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